and gave a simulation with complexity \(\frac{n^{7/3}}{\eta ^{1/3}}n^{o(1)}\) , whereas Ref. [1]} gave an interaction-picture approach with cost \(\mathcal {O}\left(\frac{n^{8/3}}{\eta ^{2/3}}\mathrm {polylog}(n)\right)\) . Our new result matches these when \(\eta \)  and \(n\)  are comparable to each other, but can be much more efficient in the regime where \(\eta \)  is much smaller than \(n\) .
